Abstract: The compound Poisson-Geometric risk model is more appropriate for describing the case that risk event and claim event are not equivalent,so it has significant background in insurance practice.In this paper the authors investigate the Poisson-Geometric risk model perturbed by diffusion under heavy-tailed claims,and the asymptotic expression satisfied by the ruin probability is derived.The result obtained in the present paper is consistent with the classical risk model perturbed by diffusion.

Key words: heavy-tailed distribution, compound Poisson-Geometric risk model, ruin probability